Lifetimes and Emergence/Decay Rates of Star Spots on Solar-type Stars Estimated by Kepler Data in Comparison with Those of Sunspots

Active solar-type stars show large quasi-periodic brightness variations caused by stellar rotations with star spots, and the amplitude changes as the spots emerge and decay. The Kepler data are suitable for investigations on the emergence and decay processes of star spots, which are important to understand underlying stellar dynamo and stellar flares. In this study, we measured temporal evolutions of star spot area with Kepler data by tracing local minima of the light curves. In this analysis, we extracted temporal evolutions of star spots showing clear emergence and decay without being disturbed by stellar differential rotations. We applied this method to 5356 active solar-type stars observed by Kepler and obtained temporal evolutions of 56 individual star spots. We calculated lifetimes, emergence and decay rates of the star spots from the obtained temporal evolutions of spot area. As a result, we found that lifetimes ($T$) of star spots are ranging from 10 to 350 days when spot areas ($A$) are 0.1-2.3 percent of the solar hemisphere. We also compared them with sunspot lifetimes, and found that the lifetimes of star spots are much shorter than those extrapolated from an empirical relation of sunspots ($T\propto A$), while being consistent with other researches on star spot lifetimes. The emerging and decay rates of star spots are typically $5 \times 10^{20}$ $\rm Mx\cdot h^{-1}$ ($8$ $\rm MSH\cdot h^{-1}$) with the area of 0.1-2.3 percent of the solar hemisphere and are mostly consistent with those expected from sunspots, which may indicate the same underlying processes.